One Problem Connected with the Helgason Support Problem

被引：0

作者：

Volchkov, V. V. ^{[1
]}

Volchkov, Vit. V. ^{[1
]}

Savost'yanova, I. N. ^{[1
]}

机构：

[1] Donetsk Natl Univ, Donetsk, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2016年 / 67卷 / 09期

关键词：

Symmetric Space; Hyperbolic Space; Legendre Function; Annular Region; Integral Geometry;

D O I：

10.1007/s11253-016-1157-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We solve the problem of description of the set of continuous functions in annular subdomains of the n-dimensional sphere with zero integrals over all (n - 1)-dimensional spheres covering the inner spherical cap. As an application, we establish a spherical analog of the Helgason support theorem and new uniqueness theorems for functions with zero spherical means.

引用

页码：1336 / 1348

页数：13

共 18 条

[1] [Anonymous], 1954, Higher Transcendental Functions
[2] POMPEIUS PROBLEM ON SPACES OF CONSTANT CURVATURE
BERENSTEIN, CA
ZALCMAN, L
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1976, 30 : 113 - 130
[3] SPHERICAL MEANS IN ANNULAR REGIONS
EPSTEIN, CL
KLEINER, B
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (03) : 441 - 451
[4] ZERO INTEGRALS ON CIRCLES AND CHARACTERIZATIONS OF HARMONIC AND ANALYTIC-FUNCTIONS
GLOBEVNIK, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 317 (01) : 313 - 330
[5] Morera theorems for complex manifolds
Grinberg, EL
Quinto, ET
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 178 (01) : 1 - 22
[6] DUALITY IN INTEGRAL GEOMETRY - SOME GENERALIZATIONS OF RADON TRANSFORM
HELGASON, S
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1964, 70 (04) : 435 - &
[7] Helgason S., 1966, P US JAP SEM DIFF GE, P37
[8] Helgason S., 1984, Groups and geometric analysis
[9] Helgason S, 2011, INTEGRAL GEOMETRY AND RADON TRANSFORMS, P1, DOI 10.1007/978-1-4419-6055-9
[10] Spherical means in annular regions in the n-dimensional real hyperbolic spaces
Rawat, Rama
Srivastava, R. K.
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2011, 121 (03): : 311 - 325

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